Logic part of talk - outline
-
First we will present
a grammar for mathematical objects.
- Then we present the semantics for the mathematical objects.
This is done by
- first introducing substitution
- next reduction
We will define reduction on instances of Math.
The basic reductions are selecting an element of a pair and
applying an abstraction to an argument.
- Subsequently, the notion context is needed.
- next unfolding
- Then the real type inference
In order to obtain meaningful mathematical expressions, we will
define typing rules for instances of Math. The type of a term depends
on a context in which the known mathematical notions are collected.
- Examples
We will present examples of representations of several mathematical
notions in the type system. To illustrate how the parameters determine
the set of derivable expressions, we present with each example a 'minimal'
sufficient type system. This means that we can represent all mathematical
notions of the example in its type system, and that we cannot do this
if we leave out a rule, an axiom or a special symbol.
-
convenience
shorter notation, searches, etc.
- discussion